On the geometry dependence of the nuclear magnetic resonance chemical shift of mercury in thiolate complexes: A relativistic density functional theory study

Thiolate containing mercury(II) complexes of the general formula [Hg(SR)n $$ {}_n $$ ]2 - n $$ {}^{2-n} $$ have been of great interest since the toxicity of mercury was recognized. 199Hg nuclear magnetic resonance spectroscopy (NMR) is a powerful tool for characterization of mercury complexes. In this work, the Hg shielding constants in a series of [Hg(SR)n $$ {}_n $$ ]2 - n $$ {}^{2-n} $$ complexes are therefore investigated computationally with particular emphasis on their geometry dependence. Geometry optimizations and NMR chemical shift calculations are performed at the density functional theory (DFT) level with both the zeroth-order regular approximation (ZORA) and four-component relativistic methods. The four exchange-correlation (XC) functionals PBE0, PBE, B3LYP, and BLYP are used in combination with either Dyall's Gaussian-type (GTO) or Slater-type orbitals (STOs) basis sets. Comparing ZORA and four-component calculations, one observes that the calculated shielding constants for a given molecular geometry have a constant difference of∼ $$ \sim $$ 1070 ppm. This confirms that ZORA is an acceptable relativistic method to compute NMR chemical shifts. The combinations of four-component/PBE0/v3z and ZORA/PBE0/QZ4P are applied to explore the geometry dependence of the isotropic shielding. For a given coordination number, the distance between mercury and sulfur is the key factor affecting the shielding constant, while changes in bond and dihedral angles and even different side groups have relatively little impact.

Extreme NMR shielding in fluoro-nitrogen cations

The structure and NMR shielding of a set of N-F containing cations is reported to near-quantitative accuracy from extensive ab initio calculations. Currently, the shortest experimentally confirmed N-F bond is 1.2461(10) Å in NNF+, however CCSD(T)-F12b/cc-pVQZ-F12 optimised geometries suggest that even shorter N-F bonds are possible for both monocations (1.236 Å, HNF+) and dications (1.098 Å, NF2+). NMR shielding constants have been calculated in a composite manner with individual components from coupled-cluster expansions up to CCSDTQP and basis sets up to aug-cc-pCV8Z, together with vibrational and relativistic corrections. 15N and 19F NMR chemical shifts correlate well with available experimental data. Extreme 19F chemical shifts are predicted for HNF+ (1628.9 ppm) and NH2F2+ (1298.0 ppm), which are by far the largest 19F chemical shifts ever reported and well outside the known range of +865 ppm (F2O2) to -448 ppm (ClF). The 15N chemical shift of -1283.07 ppm in HNF+ is similarly extreme, being well outside the known range of 15N chemical shifts of -730 to 260 ppm (CH3NO2 reference). This work highlights the application of state-of-the-art theoretical techniques, and provides accurate NMR properties of both isolated and yet unknown N-F cations, which can serve to guide and supplement NMR experimentation.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Computational 199 Hg NMR

Theoretical background and fundamental results dealing with the computation of mercury chemical shifts and spin-spin coupling constants are reviewed with a special emphasis on their stereochemical behavior and applications.

Computational 1 H and 13 C NMR in structural and stereochemical studies

Present review outlines the advances and perspectives of computational ¹ H and ¹³ C NMR applied to the stereochemical studies of inorganic, organic, and bioorganic compounds, involving in particular natural products, carbohydrates, and carbonium ions. The first part of the review briefly outlines theoretical background of the modern computational methods applied to the calculation of chemical shifts and spin-spin coupling constants at the DFT and the non-empirical levels. The second part of the review deals with the achievements of the computational ¹ H and ¹³ C NMR in the stereochemical investigation of a variety of inorganic, organic, and bioorganic compounds, providing in an abridged form the material partly discussed by the author in a series of parent reviews. Major attention is focused herewith on the publications of the recent years, which were not reviewed elsewhere.

Four-component relativistic calculations of NMR shielding constants of the transition metal complexes. Part 1: Pentaammines of cobalt, rhodium, and iridium

The nonrelativistic and four-component fully relativistic calculations of ¹ H, ¹⁵ N, ⁵⁹ Co, ¹⁰³ Rh, and ¹⁹³ Ir shielding constants of pentaammineaquacomplexes of cobalt(III), rhodium(III), and iridium(III) were carried out at the density functional theory (DFT) level of theory. The noticeable deshielding relativistic corrections were observed for nitrogen shielding constants (chemical shifts), whereas those corrections were found to be negligible for protons. For the transition metals cobalt, rhodium, and iridium, relativistic corrections to their nuclear magnetic resonance (NMR) shielding constants were found to be rather small for cobalt and rhodium (some 5-10%), whereas they are essentially larger for iridium (up to 70%).

Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding tensors and shifts in a nonrelativistic and scalar-relativistic density functional theory framework. For the latter, we make use of the scalar exact two-component Hamiltonian in its local approximation, and generally we apply the well established (multipole-accelerated) resolution of the identity approximation and the seminumerical exchange approximation. The perturbed density matrix of a paramagnetic NMR shielding calculation is further used to study the magnetically induced current density and ring currents of open-shell systems as illustrated for [U@Bi₁₂]^3-. [U@Bi₁₂]^3- features delocalized highest occupied molecular orbitals and sustains a net diatropic ring current of ca. 18 nA/T through the Bi₁₂ torus similar to the all-metal aromatic heavy-element cluster [Th@Bi₁₂]^4-.

The aug-cc-pVTZ-J basis set for the p-block fourth-row elements Ga, Ge, As, Se, and Br

The aug-cc-pVTZ-J basis set family is extended to include the fourth-row p-block elements Ga, Ge, As, Se, and Br. We use the established approach outlined by Sauer and coworkers (J. Chem. Phys. 115, 1324 [2001], J. Chem. Phys. 133, 054308 [2010], J. Chem. Theory Comput. 7, 4070 [2011], and J. Chem. Theory Comput. 7, 4077 [2011]) where the completely uncontracted aug-cc-pVTZ basis set is saturated with tight s-, p-, d-, and f-functions to form the aug-cc-pVTZ-Juc basis set for the tested elements. The saturation is carried out on the simplest hydrides possible for the tested elements GaH, GeH₄ , AsH₃ , H₂ Se, and HBr until an improvement is less than 0.01% for all s-, p-, and d-functions added. f-Functions are added to an improvement less than or equal to 1.0% due to the computational expense these functions add. The saturated aug-cc-pVTZ-Juc (26s16p12d5f) is then recontracted using the molecular orbital coefficients from self-consistent field calculations on the simple hydrides to improve computational efficiency. During contraction of the basis set, we observe that the linear hydrogen bromide molecule has a slower convergence than the other tested molecules which sets a limit on the accuracy obtained. All calculations with the contracted aug-cc-pVTZ-J [17s10p7d5f] gives results that are within 1.0% of the uncontracted results at considerable computational savings.

Efficient J-oriented tin basis sets for the correlated calculations of indirect nuclear spin-spin coupling constants

New J-oriented tin basis sets, acvXz-J (X = 2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data.

NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 10¹⁹ T J^-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the ¹J(¹¹⁹Sn, ³¹P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

First-Principles Calculation of 1H NMR Chemical Shifts of Complex Metal Polyhydrides: The Essential Inclusion of Relativity and Dynamics

1H NMR spectroscopy has become an important technique for the characterization of transition-metal hydride complexes, whose metal-bound hydrides are often difficult to locate by X-ray diffraction. In this regard, the accurate prediction of 1H NMR chemical shifts provides a useful, but challenging, strategy to help in the interpretation of the experimental spectra. In this work, we establish a density-functional-theory protocol that includes relativistic, solvent, and dynamic effects at a high level of theory, allowing us to report an accurate and reliable interpretation of 1H NMR hydride chemical shifts of iridium polyhydride complexes. In particular, we have studied in detail the hydride chemical shifts of the [Ir6(IMe)8(CO)2H14]2+ complex in order to validate previous assignments. The computed 1H NMR chemical shifts are strongly dependent on the relativistic treatment, the choice of the DFT exchange-correlation functional, and the conformational dynamics. By combining a fully relativistic four-component electronic-structure treatment with ab initio molecular dynamics, we were able to reliably model both the terminal and bridging hydride chemical shifts and to show that two NMR hydride signals were inversely assigned in the experiment.

Importance of Triples Contributions to NMR Spin-Spin Coupling Constants Computed at the CC3 and CCSDT Levels

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin-spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1-3%, but much higher corrections were found for ¹J_CN in FCN, 15.7%, and ¹J_OF in OF₂, 6.4%. The changes vary significantly in the case of multibond couplings, with differences of up to 10%, and even 13.6% for ³J_FH in fluoroacetylene. Calculations at the coupled cluster singles, doubles, and triples (CCSDT) level indicate that the most important contributions arising from connected triple excitations in the coupled cluster expansion are accounted for at the CC3 level. Thus, we believe that the CC3 method will become the standard approach for the calculation of reference values of nuclear spin-spin coupling constants.

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework

The implementation of second-order magnetic properties in a frozen density embedding scheme in a four component relativistic framework is outlined and applied to model H₂X–H₂O systems (X = Se, Te, Po).